Module type Set.S

module type S = sig .. end

Output signature of the functor Set.Make.

type elt

The type of the set elements.

type t

The type of sets.

val empty : t

The empty set.

val is_empty : t -> bool

Test whether a set is empty or not.

val mem : elt -> t -> bool

mem x s tests whether x belongs to the set s.

val add : elt -> t -> t

add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged (the result of the function is then physically equal to s).

val singleton : elt -> t

singleton x returns the one-element set containing only x.

val remove : elt -> t -> t

remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged (the result of the function is then physically equal to s).

val union : t -> t -> t

Set union.

val inter : t -> t -> t

Set intersection.

val disjoint : t -> t -> bool

Test if two sets are disjoint.

val diff : t -> t -> t

Set difference: diff s1 s2 contains the elements of s1 that are not in s2.

val compare : t -> t -> int

Total ordering between sets. Can be used as the ordering function for doing sets of sets.

val equal : t -> t -> bool

equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

val subset : t -> t -> bool

subset s1 s2 tests whether the set s1 is a subset of the set s2.

val iter : (elt -> unit) -> t -> unit

iter f s applies f in turn to all elements of s. The elements of s are presented to f in increasing order with respect to the ordering over the type of the elements.

val map : (elt -> elt) -> t -> t

map f s is the set whose elements are f a0,f a1... f
        aN, where a0,a1...aN are the elements of s.

The elements are passed to f in increasing order with respect to the ordering over the type of the elements.

If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.)

val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a

fold f s init computes (f xN ... (f x2 (f x1 init))...), where x1 ... xN are the elements of s, in increasing order.

val for_all : (elt -> bool) -> t -> bool

for_all f s checks if all elements of the set satisfy the predicate f.

val exists : (elt -> bool) -> t -> bool

exists f s checks if at least one element of the set satisfies the predicate f.

val filter : (elt -> bool) -> t -> t

filter f s returns the set of all elements in s that satisfy predicate f. If f satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s).

val filter_map : (elt -> elt option) -> t -> t

filter_map f s returns the set of all v such that f x = Some v for some element x of s.

For example,

filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s

is the set of halves of the even elements of s.

If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s.

val partition : (elt -> bool) -> t -> t * t

partition f s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate f, and s2 is the set of all the elements of s that do not satisfy f.

val cardinal : t -> int

Return the number of elements of a set.

val elements : t -> elt list

Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to Set.Make.

val min_elt : t -> elt

Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty.

val min_elt_opt : t -> elt option

Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the set is empty.

val max_elt : t -> elt

Same as Set.S.min_elt, but returns the largest element of the given set.

val max_elt_opt : t -> elt option

Same as Set.S.min_elt_opt, but returns the largest element of the given set.

val choose : t -> elt

Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

val choose_opt : t -> elt option

Return one element of the given set, or None if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

val split : elt -> t -> t * bool * t

split x s returns a triple (l, present, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; present is false if s contains no element equal to x, or true if s contains an element equal to x.

val find : elt -> t -> elt

find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists.

val find_opt : elt -> t -> elt option

find_opt x s returns the element of s equal to x (according to Ord.compare), or None if no such element exists.

val find_first : (elt -> bool) -> t -> elt

find_first f s, where f is a monotonically increasing function, returns the lowest element e of s such that f e, or raises Not_found if no such element exists.

For example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e of s where Ord.compare e x >= 0 (intuitively: e >= x), or raise Not_found if x is greater than any element of s.

val find_first_opt : (elt -> bool) -> t -> elt option

find_first_opt f s, where f is a monotonically increasing function, returns an option containing the lowest element e of s such that f e, or None if no such element exists.

val find_last : (elt -> bool) -> t -> elt

find_last f s, where f is a monotonically decreasing function, returns the highest element e of s such that f e, or raises Not_found if no such element exists.

val find_last_opt : (elt -> bool) -> t -> elt option

find_last_opt f s, where f is a monotonically decreasing function, returns an option containing the highest element e of s such that f e, or None if no such element exists.

val of_list : elt list -> t

of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements.

Iterators

val to_seq_from : elt -> t -> elt Seq.t

to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above.

val to_seq : t -> elt Seq.t

Iterate on the whole set, in ascending order

val to_rev_seq : t -> elt Seq.t

Iterate on the whole set, in descending order

val add_seq : elt Seq.t -> t -> t

Add the given elements to the set, in order.

val of_seq : elt Seq.t -> t

Build a set from the given bindings